In　view　of　the　issue　that　the　placement　of　the　platform　of　a　mobile　manipulator　has　a　great　influence　on　whether　the　manipulator　can　perform　a　given　task,　the　optimization　of　the　platform　placement　was　studied.　Firstly,　the　workspace　of　a　redundant　manipulator　was　investigated,　and　the　manipulation　capability　of　the　redundant　manipulator　was　maximized　based　on　the　manipulability　index　through　the　joint　self-motion　of　the　redundant　manipulator.　Secondly,　the　maximum　manipulation　capability　at　the　specified　work　point　was　determined.　Thirdly,　the　relative　manipulability　index　(RMI)　was　defined　by　analyzing　the　manipulation　capability　of　the　manipulator　in　its　workspace,　and　the　global　manipulability　map　(GMM)　was　presented　based　on　the　above　analysis.　Moreover,　the　optimal　platform　placement　related　to　the　given　task　was　determined,　and　motion　planning　was　implemented　by　an　improved　rapidly-exploring　random　trees　(RRT)　algorithm,　which　can　enhance　the　manipulation　capability　from　the　initial　point　to　the　target　point.　The　feasibility　of　the　proposed　algorithm　was　illustrated　with　numerical　simulations　on　the　mobile　manipulator.